Should I erase iPhone that is in lost mode? Before the power goes off?

If your passcode is truly secure and not easily guessed, there’s really no compelling technical need to do so; your data is VERY WELL protected.

A remote erase will prevent you from ever tracking it again.

The “competing argument” is that if you’ve “written off” this phone and given up all hope of recovery, there’s no real reason to NOT erase it.

What DOES matter is to never, EVER remove the phone from your account. Doing so releases the Activation Lock and allows any “finder” to reset (erasing it to it’s “new out of the box” condition) and reuse the phone.

Ok then, that’s a “significant” bit of info.

Given your situation, a remote erase is certainly recommended.

Without a passcode, anyone who finds your phone can view ALL of your info it contains.

Not exactly sure how the “Lost Phone” PIN will behave in this exact situation; I’d think that it would protect the contents but am not 100% positive.

Fortunately, since it doesn’t have a passcode, any “finder” will NOT be able to chane your AppleID password.

However, assuming the “lost PIN” does NOT work they COULD manipulate almost anything else on your phone AND you could potentially loose all copies of anything sync’d to iCloud.

Recommend that you:

1) Perform a remote erase

2) Change your AppleID password

3) Enable 2FA if you’ve not done so already

4) Mitigate damage for any personal info which might be recovered from the phone assuming that everything on it is exposed to “bad actors”